Lecture 4 normal curve, skewness, and hypothesis

D r . R a j e e v K u m a r
M S W ( T I S S , M u m b a i ) , M . P h i l ( C I P , R a n c h i ) , U G C - J R F , P h . D . , ( I I T K h a r a g p u r )
Lecture-4: Research Methodology
Normal Curve, Z-score,
Skewness, and hypothesis

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©Dr. Rajeev Kumar 2020 2

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Application of Z score
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©Dr. Rajeev Kumar 2020
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Understanding BMI Z score with normal curve
two contrasting realities
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What happens, when curve is not normal?
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Skewed curves
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What happens in skewed curve?
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Understanding skewness and Kurtosis
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How to interpret Skewness?
 In statistics, skewness is a measure of the asymmetry of the probability
distribution of a random variable about its mean.
 In other words, skewness tells you the amount and direction of skew
(departure from horizontal symmetry).
 The skewness value can be positive or negative, or even undefined. If
skewness is 0, the data are perfectly symmetrical, although it is quite
unlikely for real-world data.
As a general rule of thumb:
 If skewness is less than -1 or greater than 1, the distribution is highly
skewed.
 If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is
moderately skewed.
 If skewness is between -0.5 and 0.5, the distribution is approximately
symmetric.

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How to interpret Kurtosis?
 Kurtosis tells you the height and sharpness of the
central peak, relative to that of a standard bell curve.
 For kurtosis, the general guideline is that if the
number is greater than +1, the distribution is too
peaked. Likewise, a kurtosis of less than –1 indicates
a distribution that is too flat.
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Practical example of right skewed curve
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Example of left skew
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Type of research and need of hypothesis
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Relation with hypothesis and normal curve
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Difference between one-tailed and two tailed
hypothesis
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Hypothesis and normal curve
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Degree of Freedom
 DF= (N-1)
 For chi square= (c-1)X (R-1)
 Why one is subtracted
 “ A number of observations that are free to vary”
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I N T H E N E X T S E S S I O N , W E W I L L D I S C U S S
T H E ‘ P ’ V A L U E , A N D C O N F I D E N C E I N T E R V A L
Continued
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Lecture 4 normal curve, skewness, and hypothesis

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